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Answer:
C
Step-by-step explanation:
Median of triangle: It is a line segment joining a vertex to the midpoint of the opposite side.
Consider ΔABC, point F id the midpoint of line segment AB and E is the midpoint of luine segment AC.
Draw line segments FC and BE(medians of triangle). G is the point where line segment FC and BE meet. Now, Join AG.
Let H be the point outside the ΔABC and AG passs through the point H such that AG intersects BC at D. BH and HC are dashed lines.
We need to show that D is the midpoint of BC. The correct logical order for proof will be:
III. GC is parallel to line segment BH and line segment BG is parallel to line segment HC.
IV. Line segment FG is parallel to line segment BH and line segment GE is parallel to line segment HC.
I. BGCH is a parallelogram as opposite sides are parallel (from III.)
II. Since, diagnols of a parallelogram bisect each other. Henc, we get BD=DC.
Therefore, D is mid pont of BC.
It implies that AD is also a median.
Hence, all the three medians that are: BE,FC and AD passes through a common vertex G.
